Nodal semimetals are a unique platform to explore topological signatures of the unusual band structure that can manifest by accumulating a nontrivial phase in quantum oscillations. Here we report a study of the de Haasvan Alphen oscillations of the candidate topological nodal line semimetal CaAgAs using torque measurements in magnetic fields up to 45 T. Our results are compared with calculations for a toroidal Fermi surface originating from the nodal ring. We find evidence of a nontrivial Berry phase shift only in one of the oscillatory frequencies. We interpret this as a Berry phase arising from the semi-classical electronic Landau orbit which links with the nodal ring when the magnetic field lies in the mirror (ab) plane. Furthermore, additional Berry phase accumulates while rotating the magnetic field for the second orbit in the same orientation which does not link with the nodal ring. These effects are expected in CaAgAs due to the lack of inversion symmetry. Our study experimentally demonstrates that CaAgAs is an ideal platform for exploring the physics of nodal line semimetals and our approach can be extended to other materials in which trivial and nontrivial oscillations are present.
We present the topology of spin-split Fermi surface of CaAgAs as determined by de Haas-van Alphen (dHvA) effect measurements combined with ab initio calculations. We have determined the torus-shaped nodal-line Fermi surface from the dHvA oscillations of $β$ and $γ$ orbits. The former orbit encircles the nodal-line, while the latter does not. Nevertheless, a nontrivial Berry phase is found for both orbits. The nontrivial phase of $β$ arises from the orbital characters, which can be expressed as a pseudospin rotating around the nodal-line. On the other hand, the phase of $γ$ is attributed to the…
Topological semimetals are characterized by protected crossings between conduction and valence bands. These materials have recently attracted significant interest because of the deep connections to high-energy physics, the novel topological surface states, and the unusual transport phenomena. While Dirac and Weyl semimetals have been extensively studied, the nodal-line semimetal remains largely unexplored due to the lack of an ideal material platform. In this paper, we report the magneto-transport properties of two nodal-line semimetal candidates CaAgAs and CaCdGe. First, our single crystallin…
The topological nodal-line semimetals (NLSMs) possess a loop of Dirac nodes in the k space with linear dispersion, different from the point nodes in Dirac/Weyl semimetals. While the quantum transport associated with the topologically nontrivial Dirac fermions has been investigated extensively, features uniquely associated with the extended nodal lines remain to be demonstrated. Here, we investigate the quantum oscillations (QOs) in the nodal-line semimetal ZrSiS, with the electron transport along the c axis, and magnetic field rotating in the ab plane. The extremal orbits identified through th…
A nodal-line semimetal phase which is enforced by the symmetries of the material is interesting from fundamental and application standpoints. We demonstrate that such a phase of matter can be engineered by a simple method: Introducing vacancies in certain configurations in common symmorphic materials leads to nonsymmorphic polymorphs with symmetry-enforced nodal lines which are immune to symmetry-preserving perturbations, such as spin-orbit coupling. Furthermore, the spectrum acquires also accidental nodal lines with enhanced robustness to perturbations. These phenomena are explained on the ba…
PbTaSe$_2$ is a unique topological material, in which the number of nodal lines is expected to change at the structural transition between the lower temperature/pressure "L" phase and the higher temperature/pressure "H" phase. We report the anomalous Nernst effect attributed to the Berry curvature of nodal lines and its change with the structural transition. In the L phase, the Nernst coefficient ($S_{yx}$) shows the step-like magnetic field dependence reminiscent of the anomalous Nernst effect of nonmagnetic Dirac/Weyl semimetals. By applying hydrostatic pressure, we discovered that the ampli…
Using first-principles density-functional theory calculations, we obtain the non-coplanar nodal loop for a single-component molecular conductor [Pd(dddt)$_2$] consisting of HOMO and LUMO with different parity. Focusing on two typical Dirac points, we present a model of an effective 2 $\times$ 2 matrix Hamiltonian in terms of two kinds of velocities associated with the nodal line. The base of the model is taken as HOMO and LUMO on each Dirac point, where two band energies degenerate and the off diagonal matrix element vanishes. The present model, which reasonably describes the Dirac cone in acc…
In topological semimetals, the valence band and conduction band meet at zero-dimensional nodal points or one-dimensional nodal rings, which are protected by band topology and symmetries. In this Rapid Communication, we introduce "nodal-link semimetals", which host linked nodal rings in the Brillouin zone. We put forward a general recipe based on the Hopf map for constructing models of nodal-link semimetal. The consequences of nodal ring linking in the Landau levels and Floquet properties are investigated.
NbP is one member of a new class of nodal loop semimetals characterized by the cooperative effects of spin-orbit coupling (SOC) and a lack of inversion center. Here transport and spectroscopic properties of NbP are evaluated using density functional theory methods. SOC together with the lack of inversion symmetry splits degeneracies, giving rise to "Russian doll nested" Fermi surfaces containing 4*10$^{-4}$ electron (hole) carriers/f.u. Due to the modest SOC strength in Nb, the Fermi surfaces map out the Weyl nodal loops. Calculated structure around T$^*$~100 K in transport properties reproduc…
Pezzini et al. reported an unconventional mass enhancement in topological nodal line semimetal ZrSiS (Nat. Phys. 14, 178 (2018), whose origin remains puzzling. In this material, strong short-range interactions might induce excitonic particle-hole pairs. Here we study the renormalization of fermion velocities and find that the mass enhancement in ZrSiS can be well understood if we suppose that ZrSiS is close to the quantum critical point between semimetal and excitonic insulator. Near this quantum critical point, the fermion velocities are considerably reduced by excitonic quantum fluctuation, …
Topological semimetals with superconducting properties provide an emergent platform to explore the properties of topological superconductors. We report magnetization, and magneto-transport measurements on high quality single crystals of transition metal dichalcogenide SnTaS2. It is a nodal line semimetal with superconducting transition below Tc = 2.9 K. Moderate anisotropy (3.1) is observed in upper critical fields along H||c and H||ab plane. In the normal state we observe large magneto-resistance and weak anti-localization effect that provide unambiguous confirmation of topological features i…
Topological nodal-line semimetals are characterized by one-dimensional lines of band crossing in the Brillouin zone. In contrast to nodal points, nodal lines can be in topologically nontrivial configurations. In this paper, we study the simplest topologically nontrivial forms of nodal line, namely, a single nodal line taking the shape of a knot in the Brillouin zone. We introduce a generic construction for various "nodal-knot semimetals", which yields the simplest trefoil nodal knot and other more complicated nodal knots in the Brillouin zone. The knotted-unknotted transitions by nodal-line re…
Weyl semimetals and nodal line semimetals are characterized by linear band touching at zero-dimensional points and one-dimensional lines, respectively. We predict that a circularly polarized light drives nodal line semimetals into Weyl semimetals. The Floquet Weyl points thus obtained are tunable by the incident light, which enables investigations of them in a highly controllable manner. The transition from nodal line semimetals to Weyl semimetals is accompanied by the emergence of a large and tunable anomalous Hall conductivity. Our predictions are experimentally testable by transport measure…
Topological semimetals with nodal line are a novel class of topological matter extending the concept of topological matter beyond topological insulators and Weyl/Dirac semimetals. Here, we show that a Floquet topological semimetal with nodal helix can be generated by irradiating graphene or the surface of a topological insulator with circularly polarized light. Nodal helix is a form of nodal line running across the Brillouin zone with helical winding. Specifically, it is shown that the dynamics of irradiated graphene is described by the time Stark Hamiltonian, which can host a Floquet topologi…
The quasiparticle spectra of interacting Weyl and nodal-line semimetals on a cubic lattice are studied using the cluster perturbation theory. By tracking the spectral functions under interaction, we find that the Weyl points will move to and meet at a specific point in one Weyl semimetal model, while in the other Weyl semimetal model they are immobile. In the nodal-line semimetals, we find that the nodal line shrinks to a point and then disappears under interaction in one-nodal-line system. When we add another nodal line to this system, we find that the two nodal lines both shrink to specific …
We study the intrinsic fully-gapped odd-parity superconducting order in doped nodal-loop materials with a torus-shaped Fermi surface. We show that the mirror symmetry, which protects the nodal loop in the normal state, also protects the superconducting state as a topological crystalline superconductor. As a result, the surfaces preserving the mirror symmetry host gapless Majorana cones. Moreover, for a Weyl loop system (two-fold degenerate at the nodal loop), the surfaces that break the mirror symmetry (those parallel to the bulk nodal loop) contribute a Chern (winding) number to the quasi-two…
We show that novel low temperature properties of bulk SmB6, including the sudden growth of the de Haas-van Alphen amplitude (and heat capacity) originating from the bulk at millikelvin temperatures and a previously unreported linear-in-temperature bulk electrical conductivity at liquid helium temperatures, signal the presence of a highly asymmetric nodal semimetal. We show how the highly asymmetric nodal semimetal can be the result of a topological transformation, of the type recently considered by Shen and Fu, occurring in a Kondo lattice with dispersionless f-electron levels and Sm vacancies…
Recently, topological semimetals become hot topic in condensed matter physics, including Dirac semimetal, Weyl semimetal, and nodal line semimetal (NLSM). In this paper, a new type of node- line semimetal - type-II NLSM is proposed based on a two-band cubic lattice model. For type-II NLSM, the zero energy bulk states have a closed loop in momentum space but the (local) Weyl cones on nodal line become tilted. The effect of magnetic field and that of correlation on type-II NLSM are studied. In particular, after considering repulsive interaction and additional spin degrees of freedom, different t…
Weyl points with monopole charge $\pm 1$ have been extensively studied, however, real materials of multi-Weyl points, whose monopole charges are higher than $1$, have yet to be found. In this Rapid Communication, we show that nodal-line semimetals with nontrivial line connectivity provide natural platforms for realizing Floquet multi-Weyl points. In particular, we show that driving crossing nodal lines by circularly polarized light generates double-Weyl points. Furthermore, we show that monopole combination and annihilation can be observed in crossing-nodal-line semimetals and nodal-chain semi…
Shift current and second harmonic generation (SHG) are nonlinear optical responses that are often used for photovoltaic effect and the detection of subtle symmetry breaking patterns in materials. It has been recently shown that topological semimetals such as Weyl semimetals with broken inversion symmetry can generate large nonlinear optical responses. In this paper, we investigate both shift current and SHG in a class of topological nodal line semimetal (NLSM) systems with broken inversion symmetry, which may arise intrinsically or via an applied electric field. It is shown that certain classe…
The ratio between the shear viscosity and the entropy $η/s$ is considered a universal measure of the strength of interactions in quantum systems. This quantity was conjectured to have a universal lower bound $(1/4π)\hbar/k_{B}$, which indicates a very strongly correlated quantum fluid. By solving the quantum kinetic theory for a nodal-line semimetal in the hydrodynamic regime, we show that $η/s\propto T$ violates the universal lower bound, scaling towards zero with decreasing temperature $T$ in the perturbative limit. We find that the hydrodynamic scattering time between collisions is nearly t…
Nodal loop semimetals are close descendants of Weyl semimetals and possess a topologically dressed band structure. We argue by combining the conventional theory of magnetic oscillation with topological arguments that nodal loop semimetals host coexisting topological and trivial magnetic oscillations. These originate from mapping the topological properties of the extremal Fermi surface cross sections onto the physics of two dimensional semi Dirac systems, stemming from merging two massless Dirac cones. By tuning the chemical potential and the direction of magnetic field, a sharp transition is i…
Recently, the nodal line semimetals have attracted considerable interests in condensed matter physics. We show that their distinct band structure can be detected by measuring the collective modes. In particular, we find that the dependence of the plasmon frequency $ω_p$ on the electron density $n$ follows a $ω_p \sim n^{1/4}$ law in the long wavelength limit. Our results will be useful in the ongoing search for new candidates of nodal line semimetals.
We have applied nuclear magnetic resonance spectroscopy to study the distinctive network of nodal lines in the Dirac semimetal ZrSiTe. The low-$T$ behavior is dominated by a symmetry-protected nodal line, with NMR providing a sensitive probe of the diamagnetic response of the associated carriers. A sharp low-$T$ minimum in NMR shift and $(T_1T)^{-1}$ provides a quantitative measure of the dispersionless, quasi-2D behavior of this nodal line. We also identify a van Hove singularity closely connected to this nodal line, and an associated $T$-induced Lifshitz transition. A disconnect in the NMR s…
The high-magnetic-field thermoelectric effect in nodal-line semimetals with straight nodal lines was investigated. Three-dimensional (3D) Dirac/Weyl semimetals exhibit constant thermoelectric Hall conductivity at the high-magnetic-field quantum limit, resulting in a boundless linear increase of Seebeck coefficient. This is known as the quantized thermoelectric Hall effect (QTHE), and is expected to lead to high-performance thermoelectricity at low temperatures. Here, in addition to Dirac/Weyl semimetals, we demonstrated that 3D semimetals with straight nodal lines can also exhibit the QTHE und…
Nodal line semimetals are characterized by nontrivial bulk-band crossings, giving rise to almost flat drumhead-like surface states (DSS), which provide an attractive playground where interaction can induce symmetry-broken states and potential emergent phases. Here, we show that electronic interaction causes Stoner ferromagnetic instability in the DSS while the bulk remains non-magnetic, which together with spin-orbit coupling drive the surface states into a 2D Chern insulator. We show that each DSS carries a half-monopole charge, which for systems containing two pieces of DSS yield a net Chern…
We show a holographic model of a strongly coupled topological nodal line semimetal (NLSM) and find that the NLSM phase could go through a quantum phase transition to a topologically trivial state. The dual fermion spectral function shows that there are multiple Fermi surfaces each of which is a closed nodal loop in the NLSM phase. The topological structure in the bulk is induced by the IR interplay between the dual mass operator and the operator that deforms the topology of the Fermi surface. We propose a practical framework for building various strongly coupled topological semimetals in holog…
Recently there have been several proposals of materials predicted to be nodal-ring semimetals, where zero energy excitations are characterized by a nodal ring in the momentum space. This class of materials falls between the Dirac-like semimetals and the more conventional Fermi-surface systems. As a step towards understanding this unconventional system, we explore the effects of the long-range Coulomb interaction. Due to the vanishing density of states at the Fermi level, Coulomb interaction is only partially screened and remains long-ranged. Through renormalization group and large-$N_f$ comput…
We investigate the impact of s-wave spin-singlet pairing on antiferromagnetic semimetals with Dirac points or nodal loops at the Fermi level. The electron pairing is generally shown to convert the semimetal into a tunable nodal superconductor. The changeover from fully gapped to gapless phases is dictated by symmetry properties of the antiferromagnetic-superconducting state that set the occurrence of a large variety of electronic topological transitions. We provide a general criterion for predicting a series of transitions between nodal and fully gapped superconducting phases. Different types …
We study an improved holographic model for the strongly coupled nodal line semimetal which satisfies the duality relation between the rank two tensor operators $\barψγ^{μν}ψ$ and $\barψγ^{μν}γ^5ψ$. We introduce a Chern-Simons term and a mass term in the bulk for a complex two form field which is dual to the above tensor operators and the duality relation is automatically satisfied from holography. We find that there exists a quantum phase transition from a topological nodal line semimetal phase to a trivial phase. In the topological phase, there exist multiple nodal lines in the fermionic spec…
Quantum oscillations in magnetoconductance of a material at low temperatures and in presence of an intense magnetic field are described by the Shubnikov de Haas (SdH) effect. It is widely assumed to be the hallmark of the Fermi surface of a given metal. In contrast to the canonical situation, we identify an exotic oscillation in nonlinear responses of three-dimensional nodal line semimetals (NLSMs) which persist even at temperatures where the typical SdH-like oscillations vanish. This oscillation occurs due to the periodic gap-closing of a pair of Landau levels at zero Fermi energy with the va…
We study the effect of short range interactions in three dimensional nodal-line semimetals with linear band crossings. We analyze the Yukawa theories for gapped instabilities in the charge, spin and superconducting channels using the Wilsonian renormalization group framework, employing a large number of fermion flavors $N_{f}$ for analytical control. We obtain stable non-trivial fixed points and provide a unified description of the critical exponents for the ordering transitions in terms of the number of order parameter components $N_{b}$ systematically to order $1/N_{f}$. We show that in all …
We study the electrical conductivity in a nodal-line semimetal with charged impurities. The screening of the Coulomb potential in this system is qualitatively different from what is found in conventional metals or semiconductors, with the screened potential $ϕ$ decaying as $ϕ\propto 1/r^2$ over a wide interval of distances $r$. This unusual screening gives rise to a rich variety of conduction regimes as a function of temperature, doping level and impurity concentration. In particular, nodal-line semimetals exhibit a diverging mobility $\propto 1/|μ|$ in the limit of vanishing chemical potentia…
Nodal semimetals (e.g. Dirac, Weyl and nodal-line semimetals, graphene, etc.) and systems of pinned particles with power-law interactions (trapped ultracold ions, nitrogen defects in diamonds, spins in solids, etc.) are presently at the centre of attention of large communities of researchers working in condensed-matter and atomic, molecular and optical physics. Although seemingly unrelated, both classes of systems are abundant with novel fundamental thermodynamic and transport phenomena. In this paper, we demonstrate that low-energy field theories of quasiparticles in semimetals may be mapped …
Thermoelectric materials intrigue much interest due to their wide range of application such as power generators and refrigerators. The efficiency of thermoelectric materials is quantified by the figure of merit, and a figure greater than unity is desired. To achieve this, a large Seebeck coefficient and low phonon thermal conductivity are required. We show that this can be achieved with a thin film of topological nodal line semimetals. We also discusses the correlation effect and spin current induced by a temperature gradient. The obtained results provide insight for the improvement of thermoe…
Topological nodal-line semimetals are predicted to exhibit unique drumhead-like surface states (DSS). Yet, a direct detection of such states remains a challenge. Here, we propose spin-resolved transport in a junction between a normal metal and a spin-orbit coupled nodal-line semimetal as the mechanism for their detection. Specifically, we find that in such a device, the DSS induce resonant spin-flipped reflection. This effect can be probed by both vertical spin transport and lateral charge transport between anti-parallel magnetic terminals. In the tunneling limit of the junction, both spin and…
We have investigated magnetotransport properties of YRh6Ge4, which was recently predicted to be a triply degenerate nodal semimetal. We find it exhibits remarkable signatures of a chiral anomaly, manifested by large negative longitudinal magnetoresistance, quadratic field dependence of magnetoconductance and planar Hall effect. Furthermore, we have also observed Shubnikov-de Haas (SdH) quantum oscillations in the magnetoresistivity measurements on this material. The analyses of the SdH data reveal two point-like Fermi surfaces and these pockets are found to host nearly massless fermions. The s…
Topological nodal line semimetals are characterized by the crossing of the conduction and valence bands along one or more closed loops in the Brillouin zone. Usually, these loops are either isolated or touch each other at some highly symmetric points. Here, we introduce a new kind of nodal line semimetal, that contains a pair of linked nodal loops. A concrete two-band model was constructed, which supports a pair of nodal lines with a double-helix structure, which can be further twisted into a Hopf link because of the periodicity of the Brillouin zone. The nodal lines are stabilized by the comb…
The effect of short-range disorder in nodal line semimetals is studied by numerically exact means. For arbitrary small disorder, a novel semimetallic phase is unveiled for which the momentum-space amplitude of the ground-state wave function is concentrated around the nodal line and follows a multifractal distribution. At a critical disorder strength, a semimetal to compressible metal transition occurs, coinciding with a multi- to single-fractality transition. The universality class of this critical point is characterized by the correlation length and dynamical exponents. At considerably higher…
The self-consistent Born approximation quantitatively fails to capture disorder effects in semimetals. We present an alternative, simple-to-use non-perturbative approach to calculate the disorder induced self-energy. It requires a sufficient broadening of the quasiparticle pole and the solution of a differential equation on the imaginary frequency axis. We demonstrate the performance of our method for various paradigmatic semimetal Hamiltonians and compare our results to exact numerical reference data. For intermediate and strong disorder, our approach yields quantitatively correct momentum re…
We propose a general framework for constructing a large set of nodal-point semimetals by tuning the number of linearly ($d_L$) and (at most) quadratically ($d_Q$) dispersing directions. By virtue of such a unifying scheme, we identify a new perturbative route to access various strongly interacting non-Dirac semimetals with $d_Q>0$. As a demonstrative example, we relate a two dimensional anisotropic semimetal with $d_L=d_Q=1$, describing the topological transition between a Dirac semimetal and a normal insulator, and its three dimensional counterparts with $d_L=1$, $d_Q=2$. We address the quant…
